Compensation for denied boarding due to baggage delay

Question

Recently, my son and I traveled from Bangkok to the US, and when boarding our connecting flight in Hong Kong we were involuntarily denied boarding because the airline could not locate my son's checked-in bag.
Long story short, the airline lost his bag then kicked us off our flight because of their mistake!

I am aware that airlines cannot transport baggage without the passenger, in the event that a passenger fails to show for the flight their bags are checked in on. But in this case, we presented our valid boarding passes showing that our bags were checked through from BKK to the US.
The airlines had 100% control of our bags and we could not have had anything to do with the missing bag. We arrived at our destination 11 hours late as a result.

When I complained and asked for compensation, they claimed that they fulfilled their obligation by paying for an alternate flight.
They admitted that the situation was mishandled and offered us $50 gift cards.

But they acted as though we were crazy for requesting the involuntary denial of boarding compensation that would have applied if we had been bumped due to the flight being oversold (which was also the case since it was a full flight and our seats were given to standby passengers). I have reached an impasse with the airline.

Additional details from the comments: I purchased R/T tickets SEA-BKK and all flights were Delta except BKK-HKG on the return (Cathay Pacific). Our bags were checked through BKK-SEA.
When boarding in HKG (6 hr stopover) we found out at the gate that my son's bag was delayed, and he was denied boarding for that reason.
The two airlines blamed each other. CP arranged our re-routing because DL did not have another flight until the next day.
Our boarding pass receipts read "involuntary re-routing" and "reason for issuance-late arriving equipment bill to Delta." My complaint to DL resulted in offers for $50 gift cards, that's all

I started with an online complaint, then an online refund request, replied to one of Delta's responses, then finally sent a letter to their executive team.
We received successive offers: $50 gift cards for each of us, $100 gift cards, $100 gift cards again, $150 gift cards plus $94 for our expenses.
I don't know yet if we can only claim one or if we get all of them (which adds up to being just $500 short of the 400%/max $1,350 compensation rule).

They say the IBD rule only applies to overbooking, but apologized without admitting fault

Answer 1

You can fly without your luggage, your luggage can fly without you if it fails to make the connection which you made, it is done often.

I guess it is a case of an airline mistake that they do not want to admit, made worse by the fact that there were two airlines involved.

It seems that you have done much already to claim compensation, and got more than you initially did, but you might be able to squeeze a bit or even a lot more out of them by going public, on twitter or some such site, or by using a consumer protection organization.

As this is a rather rare thing to happen, I think there is no standard compensation across the airlines, there might be a company standard. If you are not happy with the compensation you got so far but not want to go public, you can write a letter, send it recorded, and ask for the proper compensation.
The more official you make the letter, the better impression you make and as far as I understand these things, the more likely your letter is taken serious.